9.2. Least-Squares Regression http://www.ck12.org
3.Y=bX+a
4.− 2 .951. This regression coefficient means that every− 2 .951 percent change in memory test score is associ-
ated with a one percent change in exercise per week.
5.Yˆ=− 2. 951 X+ 13. 65- Answer to the discretion of the teacher
- If a student exercised 3 times per week, we would expect that they would have a memory test score of 4.8.
- No. A data transformation is not necessary because the relationship between the two variables is linear.
- See Table Below.
TABLE9.12:
Student Exercise Per Week Memory Test Score Predicted Value Residual Score
1 0 15 13. 7 1. 4
2 2 3 7. 7 − 4. 7
3 2 12 7. 7 4. 3
4 1 11 10. 7 0. 3
5 3 5 4. 8 0. 2
6 1 8 10. 7 − 2. 7
7 2 15 7. 7 7. 3
8 0 13 13. 7 − 0. 7
9 3 2 4. 8 − 2. 8
10 3 4 4. 8 − 0. 8
11 4 2 1. 8 0. 2
12 1 8 10. 7 − 2. 7
13 1 10 10. 7 − 0. 7
14 1 12 10. 7 1. 3
15 2 8 7. 7 0. 3- Upon first glance, a transformation of the data is not necessary since the residual values are relatively evenly
distributed on the scatterplot. However, it is worth considering dropping several one or two of the outliers
(namely observation 7) if they are over three standard deviations from the mean.